Israel's pursuit of righteousness

Romans: The Gospel for God’s glory
Romans 9:30-10:4
Israel’s pursuit of righteousness
Israel did not attain God’s righteousness for they didn’t seek it by faith

1) Gentiles who did not pursue righteousness, attained righteousness by faith, 9:30.
This is what Paul is doing in 9:30-31: “What then do we say to the fact that God has called many Gentiles but only a remnant of his chosen people, the Jews (in light of 9:1-29), who had the greatest spiritual privileges?”

2) Israel, pursuing the law for righteousness, did not attain to that law, 9:31.

3) Israel didn’t attain righteousness because they didn’t pursue the law by faith but as from works, 9:32a.
What does Paul mean by saying that Israel didn’t attain being right with God because they didn’t pursue the law by faith but as if it were works?

4) Israel has stumbled as Isaiah wrote, “I lay in Zion a stumbling stone; whoever believes in him won’t be put to shame,” 9:32b-33.
Paul quotes Isaiah 8:14 combined with Isaiah 28:16, exhorting Israel to trust in the Lord to avoid judgment. What does Paul mean in applying these words to Israel in his day?

5) The Apostle Paul’s heart’s desire and prayer for Israel was that they may be saved, 10:1.
Paul is not about to write off Israel because they have stumbled over Christ. His heart’s desire and prayer is for their salvation. Why does Paul say this? Why is it so important that we pray for lost people?

6) Israel has a zeal for God but not according to knowledge, 10:2.
Paul knows about having a zeal for God not according to knowledge, from his pre-Christ days. Talk about the idea that “it doesn’t matter what you believe as long as you’re zealous or sincere.”

7) Israel didn’t submit to God’s righteousness, being ignorant of it and seeking to establish their own, 10:3.
How does Paul explain further in v.3 what he said in v.2, that the Jews had a zeal but not according to knowledge?

8) Christ is the end of using the law for righteousness to everyone who believes, 10:4.
Following Paul’s thinking in this context, in what way(s) is Christ the end or goal of the law for righteousness to everyone who believes?